In this paper, we establish a general theta function identity. It is a common origin of many theta function identities. From which many classical and new modular equations are derived. All the proofs are elementary.
The completion of genome sequences and subsequent high-throughput mapping of molecular networks have allowed us to study biology from the network perspective. Experimental, statistical and mathematical modeling approa...The completion of genome sequences and subsequent high-throughput mapping of molecular networks have allowed us to study biology from the network perspective. Experimental, statistical and mathematical modeling approaches have been employed to study the structure, function and dynamics of molecular networks, and begin to reveal important links of various network properties to the functions of the biological systems. In agreement with these functional links, evolutionary selection of a network is apparently based on the function, rather than directly on the structure of the network. Dynamic modularity is one of the prominent features of molecular networks. Taking advantage of such a feature may simplify network-based biological studies through construction of process-specific modular networks and provide functional and mechanistic insights linking genotypic variations to complex traits or diseases, which is likely to be a key approach in the next wave of understanding complex human diseases. With the development of ready-to-use network analysis and modeling tools the networks approaches will be infused into everyday biological research in the near future.展开更多
In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are ob...In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are obtained.展开更多
New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion functio...New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus. improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.展开更多
In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
The authors prove some monotonicity properties of functions involving the generalized Agard distortion function ηg（a,t）, and obtain some inequalities for ηk（a, t） and relative distortion functions.
Background: There is much interest regarding metal-on-metal implants in medical and general media. Much of this has been regarding failure of specific implant systems and metal ion toxicity. We present our early mid-t...Background: There is much interest regarding metal-on-metal implants in medical and general media. Much of this has been regarding failure of specific implant systems and metal ion toxicity. We present our early mid-term experience of the ADEPT metal-on-metal system which has both modular and non-modular hip options. Methods: Functional assessment, blood metal ion quantification, and radiographic analysis were performed for the modular and non-modular ADEPT variants. Fifty implants were implanted with a mean follow up time of 28 months. Unpaired t-tests were used to compare modular and resurfacing groups, standardised hip scores were used to compare function to conventional total hip arthroplasty. Results: Metal ion levels were significantly higher in modular prostheses compared to resurfacing implants, but not at “harmful” levels (as determined by a previous metal-on-metal implant recall). Functional outcomes were excellent and revision rates were lower than expected. Conclusions: At our institution we have good outcomes with the ADEPT hip prosthesis. Though patient selection and implant position are crucial, poor performance of metal-on-metal hip replacements is implant specific.展开更多
基金Supported by the National Natural Science Foundation of China（11071107, 11371184）
文摘In this paper, we establish a general theta function identity. It is a common origin of many theta function identities. From which many classical and new modular equations are derived. All the proofs are elementary.
文摘The completion of genome sequences and subsequent high-throughput mapping of molecular networks have allowed us to study biology from the network perspective. Experimental, statistical and mathematical modeling approaches have been employed to study the structure, function and dynamics of molecular networks, and begin to reveal important links of various network properties to the functions of the biological systems. In agreement with these functional links, evolutionary selection of a network is apparently based on the function, rather than directly on the structure of the network. Dynamic modularity is one of the prominent features of molecular networks. Taking advantage of such a feature may simplify network-based biological studies through construction of process-specific modular networks and provide functional and mechanistic insights linking genotypic variations to complex traits or diseases, which is likely to be a key approach in the next wave of understanding complex human diseases. With the development of ready-to-use network analysis and modeling tools the networks approaches will be infused into everyday biological research in the near future.
文摘In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are obtained.
基金Supported by National 973 Project of China(2006CB708304)National Natural Science Foundation of China(10771195)
文摘New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus. improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.
基金Supported by the National Natural Science Foundation of China(11071069, 11171307)the Natural Science Foundation of Hunan Province(09JJ6003)
文摘In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
基金supported by the Natural Science Foundation of China(11071069 and 11171307)the Natural Science Foundation of the Department of Education of Zhejiang Province(Y201328799)
文摘The authors prove some monotonicity properties of functions involving the generalized Agard distortion function ηg（a,t）, and obtain some inequalities for ηk（a, t） and relative distortion functions.
文摘Background: There is much interest regarding metal-on-metal implants in medical and general media. Much of this has been regarding failure of specific implant systems and metal ion toxicity. We present our early mid-term experience of the ADEPT metal-on-metal system which has both modular and non-modular hip options. Methods: Functional assessment, blood metal ion quantification, and radiographic analysis were performed for the modular and non-modular ADEPT variants. Fifty implants were implanted with a mean follow up time of 28 months. Unpaired t-tests were used to compare modular and resurfacing groups, standardised hip scores were used to compare function to conventional total hip arthroplasty. Results: Metal ion levels were significantly higher in modular prostheses compared to resurfacing implants, but not at “harmful” levels (as determined by a previous metal-on-metal implant recall). Functional outcomes were excellent and revision rates were lower than expected. Conclusions: At our institution we have good outcomes with the ADEPT hip prosthesis. Though patient selection and implant position are crucial, poor performance of metal-on-metal hip replacements is implant specific.
